Find the Point(s) on the Curve Described by the Vector $\mathbf { r } ( t ) = \left\langle t ^ { 2 } + 2 t , t ^ { 3 } - 12 t \right\rangle$

Essay

Find the point(s) on the curve described by the vector function $\mathbf { r } ( t ) = \left\langle t ^ { 2 } + 2 t , t ^ { 3 } - 12 t \right\rangle$ where the tangent vector is horizontal or vertical.